Question

A triangle has corners at `(5 ,2 )`, `(4 ,1 )`, and `(3 ,8 )`. How far is the triangle's centroid from the origin?

Answer 1

Triangle's centroid is `5.426` units away from the origin.

Explanation:

Centroid of a triangle, whose corners are `(x_1,y_1)`, `(x_2,y_2)` and `(x_3,y_3)`, is given by `(1/3(x_1+x_2+x_3),1/3(y_1+y_2+y_3))`

Hence centroid of the triangle whose corners are `(5,2)`, `(4.1)` and `(3,8)` is

`(1/3(5+4+3),1/3(2+1+8))` or `(12/3,11/3)`

And its distance from origin `(0,0)` is

`sqrt((12/3-0)^2+(11/3-0)^2)=sqrt(144/9+121/9)`

= `1/3sqrt265=1/3xx16.279=5.426`